Before a computer is assembled, its motherboard goes through a special inspection. Assume only 85% of motherboards pass this inspection.(a) What is the probability that at least 13 of the next 15 motherboards pass inspection?
(b) On the average, how many motherboards should be inspected until a motherboard that passes inspection is found?

Answers

Answer 1

Answer:

a. The probability that at least 13 of the next 15 motherboards pass inspection is 0.604.

b. On average, 1.1765 motherboards should be inspected until a motherboard that passes inspection is found.

The formula for the probability of getting exactly k successes in n trials with a success probability of p is:

$P(X = k) = (^nC_k) * p^k * (1 - p)^((n - k))$

Where "n choose k" represents the binomial coefficient, which is calculated as n! / (k! * (n - k)!), where "!" denotes factorial.

In this case:

n = 15 (number of trials)

k = 13, 14, 15 (number of successes)

p = 0.85 (probability of success)

First, let's calculate the probability that exactly 13, 14, and 15 motherboards pass inspection.

For k = 13:

$P(X = 13) = (^(15) C_ {13}) * 0.85^(13) * (1 - 0.85)^((15 - 13))$

= 0.28564

For k = 14:

$P(X = 14) = (^(15) C_(14)) * 0.85^(14) * (1 - 0.85)^((15 - 14))$

= 0.23123

For k = 15:

$P(X = 15) = (^(15) C_(15)) * 0.85^(15) * (1 - 0.85)^((15 - 15))$

= 0.08735

Now, sum these probabilities to get the final answer:

P(at least 13) = P(X = 13) + P(X = 14) + P(X = 15)

= 0.28564 + 0.23123 + 0.08735

= 0.60422

= 0.604

(b)

The average number of trials needed until a motherboard that passes inspection is found can be calculated using the concept of the expected value of a geometric distribution:

Expected value (E) = 1 / p

Where p is the probability of success.

In this case, p = 0.85.

E = 1 / 0.85

= 1.1765

Thus, on average, 1.1765 motherboards should be inspected until a motherboard that passes inspection is found.

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Answer 2

Answer:

Final answer:

To find the probability that at least 13 of the next 15 motherboards pass the inspection, use the binomial formula for each scenario (13, 14, and 15 passing) and sum the results. To find on average how many motherboards need to be inspected for one to pass inspection, just take the reciprocal of the probability of success (1/0.85).

Explanation:

This question falls under the domain of probability and statistics. Let's tackle each part separately:

(a) When we talk about at least 13 out of 15 motherboards passing, we have to consider the situations where exactly 13, 14, or all 15 pass. For each case, you would use the binomial formula P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)). In this formula, n is the number of trials (which is 15), k is the number of successes we are interested in, p is the probability of a success (which is 0.85), C(n, k) is a combination that represents the different ways k successes can happen in n trials. Calculate this for k = 13, 14, and 15 and sum the results to get the probability for at least 13 to pass.

(b) To find on average how many motherboards should be inspected until one passes is straightforward - it is simply the reciprocal of the probability of success which is 1/0.85.

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Another rock in Death Valley at the Racetrack traveled 55.3 meters during the observation period of nine years. a . What was the rock's average speed in feet per year? Round your answer to the nearest whole number. feet per year b . If a strong wind gives a stone an initial velocity of v 0 = 11 m / s , and the friction coefficient of stone on ice is μ = 0.14 , and g = 9.81 m / s 2 . Use the equation v 2 0 = 2 μ g S to find the stopping distance S for the stone. Round your answer to the nearest tenth.

Answers

Answer:

a) 20 feet per year

b) 44.1 m

Step-by-step explanation:

Given:

Distance traveled during the observation period = 55.3 meters

Observation period = 9 years

initial velocity of v₀ = 11 m/s

friction coefficient of stone on ice is μ = 0.14

g = 9.81 m/s²

also,

v₀² = 2μgS

Now,

1 m = 3.28084 ft

thus,

Total distance in feet = 55.3 × 3.28084 = 181.430452 ft

Average speed = $\frac{\textup{Distance}}{\textup{Time}}$

Average speed = $\frac{\textup{181.430452}}{\textup{9}}$

Average speed = 20.159 feet/year ≈ 20 feet per year

b) v₀² = 2μgS

substituting the values in the above equation, we get

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s = 44.051 ≈ 44.1 m

A water tank leaked 14 gallons of water over eight hours at a constant rate what was the change in the amount of water in gallons in a tank each hour

Answers

Answer:

7/4 gallons per hour

Step-by-step explanation:

We have to divide the amount of water lost by the lapse of time. So we get

14/8= 7/4

Answer: the answer would be 1.75 gallons/hour

Step-by-step explanation: if you take the 14 gallons divided by the eight hours, you get 1.75

Sara needs 40 inches of yarn to glue onto each of 25 picture frames. She has a ball of yarn with a total of 950 inches. Which of the following explains whether Sara has enough yarn to glue onto all 25 picture frames?A. Because 950 ÷ 40 = 24 R10, she has enough yarn for all 25 picture frames.

B. Because 950 ÷ 40 = 24 R10, she has enough yarn for only 24 picture frames.

C. Because 950 ÷ 40 = 23 R30, she has enough yarn for only 23 picture frames.

D. Because 950 ÷ 40 = 23 R30, she has enough yarn for only 24 picture frames.

Answers

Answer:

C. Because 950 ÷ 40 = 23 R30, she has enough yarn for only 23 picture frames.

Step-by-step explanation:

950/40 = 23.75 = 23 r 30

Sara has enough for 23 frames.

Answer:

C. Because 950 ÷ 40 = 23 R30, she has enough yarn for only 23 picture frames.

Step-by-step explanation:

950/40 = 23.75 = 23 r 30

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Victor collects data on the price of a dozen eggs at 8 different stores.median: $ 1.55
Find the lower quartile and upper quartile of
the data set.
lower quartile: $
upper quartile: S
?
$1.39 $1.40 $1.44 $1.50 $1.60 $1.63 $1.65 $1.80

Answers

Answer:

Lower quartile: $1.42

Upper quartile: $1.64

Step-by-step explanation:

The median is the middle value when all data values are placed in order of size.

The ordered data set is:

$1.39 $1.40 $1.44 $1.50 $1.60 $1.63 $1.65 $1.80

There are 8 data values in the data set, so this is an even data set.

Therefore, the median is the mean of the middle two values:

$\implies \sf Median\;(Q_2)=(\$1.50+\$1.60)/(2)=\$1.55$

Place "||" in the middle of the data set to signify where the median is:

$1.39 $1.40 $1.44 $1.50 ║ $1.60 $1.63 $1.65 $1.80

The lower quartile (Q₁) is the median of the data points to the left of the median. As there is an even number of data points to the left of the median, the lower quartile is the mean of the the middle two values:

$\implies \sf Lower\;quartile\;(Q_1)=(\$1.40+\$1.44)/(2)=\$1.42$

The upper quartile (Q₃) is the median of the data points to the right of the median. As there is an even number of data points to the right of the median, the upper quartile is the mean of the the middle two values:

$\implies \sf Upper \;quartile\;(Q_1)=(\$1.63+\$1.65)/(2)=\$1.64$

Answer:

to find the lower quartile and upper quartile of the given dataset, we need to first arrange the data in ascending order:

$1.39, 1.40, 1.44, 1.50, 1.60, 1.63, 1.65, 1.80$

The median of the dataset is given as $1.55$. Since there are an even number of data points, the median is the average of the two middle values, which in this case are $1.50$ and $1.60$.

Now, we need to find the lower quartile and upper quartile. The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half of the data set.

The lower half of the dataset is $1.39, 1.40, 1.44, 1.50$. The median of this half is the average of the middle two values, which are $1.40$ and $1.44$.

Therefore, the lower quartile is $1.42$.

The upper half of the dataset is $1.60, 1.63, 1.65, 1.80$. The median of this half is the average of the middle two values, which are $1.63$ and $1.65$.

Therefore, the upper quartile is $1.64$.

Hence, the lower quartile of the dataset is $1.42$ and the upper quartile is $1.64$.

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Answers

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Answers

Answer:

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Step-by-step explanation:

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